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Computations of properties of twin planes in silver halide
0022-3697(95)00257-X
Pergamon
COMPUTATIONS
.I Phys. Chem Solids Vol57. No 5, pp. 627-634.1996 Copyright 0 1996 Eastman Kodak Company. Published by Elswier Science Ltd Printed in Great Britain. All nghts reserved 0022-3697196 $15 00 + 0.00
OF PROPERTIES OF TWIN IN SILVER HALIDE
PLANES
ROGER C. BAETZOLD Imaging Research and Advanced Development, Eastman Kodak Company, Rochester, NY 14650, U.S.A (Received 2 April 1995; accepted 11 July 1995)
Abstract-Computer simulations have been applied to treat the defect properties influenced by twin planes in silver halide. The formation energy of silver and halide twin planes is roughly equal in AgCI, but halide is significantly smaller in AgBr. The Madelung potential is attenuated at twin planes, promoting electron trapping at silver and hole trapping at halide twin planes. The formation energy of components of the Frenkel defect is reduced at the twin plane relative to the perfect crystal. Keywords:
A. inorganic compounds, A. semiconductors, D. crystal structure, D. defects.
1. INTRODUCTION
by
Twin planes are present in most tabular silver halide
grains. They have been observed experimentally [l-3] through various diffraction experiments and detected in transmission electron microscopy (TEM) crosssection experiments [4]. In fact, the growth of tabular grains has been explained through models [S] that require the presence of twin planes. These models consider that, because of special properties of the sites where twin planes intersect the surface, there will be preferential deposition of ions from solution as compared to sites on flat surfaces. Frequently, a doubly twinned plane is present in grains as observed in electron diffraction [6,7]. This structure can grow in a self-perpetuating manner. Owing to the ubiquitous presence of twin planes, one can contemplate their possible role in the photographic effect. So far, a complete understanding of this role is lacking. Consider specifically how {111) layers of a rock salt structure such as silver halide assemble. Any { 111) layer is composed of ions of all the same type and having a spacing of &a, where a is the nearestneighbor distance. The ions in this layer are positioned to form equilateral triangles on sites we shall designate as A, as shown in Fig. 1. Now ions of the opposite charge forming adjacent layers may bind at various sites above this layer. For ionic binding, the hollow sites are preferred [8], and are designated B or C in Fig. 1. Once either choice is made, additional ions are deposited in registry to complete this {111) layer. Ions for the third layer alternate again in sign and deposit at the B or C site unoccupied by the second layer, or the A site [9]. The perfect fee rock salt crystal structure has a site occupancy on {111) layers given
ABCABCABC
(1)
Now consider the site occupancy taken at a twin plane. Here, we begin by the normal ABC sequence, but then the next layer occupies a B site rather than the expected A site and the growth sequence now becomes BAC. ABCABCBACBAC
(2)
such that the C layer becomes the twin plane and there is reflection symmetry across this twin plane, referred to as a stacking fault. We may also note another potential type of stacking fault. Suppose that after the B sites are occupied, the original growth sequence of ABC is retained. This results in the pattern ABCABCBCABCABC
(3)
This stacking fault has two adjacent layers with an incorrect placement of ions (BCB) and (CBC). One should expect this stacking fault to have roughly twice the energy of formation of the twin plane, since the surface area containing the defect is doubled and therefore, less probable. Let us consider how the presence of twin planes changes the interactions in a crystal. Because it is the next-nearest neighbors that have a changed relative placement due to the twin planes, we expect the perturbations to be short ranged. In the perfect crystal, the distance between next-nearest neighbors is &a versus 2a/fi at the twin plane, as sketched in Fig. l(b). The next-nearest neighbor ions have the 627
R. C. BAETZOLD
628
m
A
(a)
0.
.c
(W
:
2. METHOD
:
I
I
I
I I
d
d
I
PERFECT
impurity segregation, or point defect properties. Finally, we note that two types of twin planes are possible as characterized by whether a halide or silver ion is on the twin plane.
TWIN PLANE
Fig. 1. A segment of the {111) layer of a silver halide plane is shown with ions at sites designated A. The sites B or C in the center of equilateral triangles are available for growth of the next layer. In (b) the next-nearest neighbor positions denoted X are shown for perfect and twin planes. same charge. In the unrelaxed crystal, these ions are positioned 18% closer. This distortion will cause a significant change in the interatomic interaction that is based on electrostatic, polarization, and short-range terms. The crystal will be forced to relax in this region to achieve a zero force structure. Also, because the interatomic terms differ for silver and halide ions, the properties of silver and halide ion twin planes will be different. Photolysis of unsensitized silver bromide grains often leads to silver formation at twin planes. This has been revealed experimentally using electron microscopy to study protrusions on a heavily exposed grain [lo]. These experiments imply some special electronic properties for twin planes that influence photocarriers or facilitate the growth of silver. However, because the exposure levels are much greater than those employed in typical photographic experiments, it is unclear whether the twin planes are important in the latter process. On the other hand, experiments [l l] at lower light exposures have given evidence for formation of photolytic silver and were interpreted to indicate effective electron trapping sites along the twin plane. The purpose of this report is to provide some initial studies of the structure and electronic properties of twin planes in silver halide. It has not been clear whether twin planes should introduce any electronic perturbation that would significantly effect electronic or ionic defects. There are other questions that arise concerning the geometric distortions at a twin plane and whether the possible strain introduced into a crystal would change carrier trapping properties,
The method employed in these calculations to simulate twin planes involves constructing a supercell within a three-dimensional infinite representation. The large cell contains a chain of ions placed according to eqn (2). The translation vectors (a, O,O)a, (l/a, fl, 0) a, and (0,0,z) a (where z is the repeat distance on the chain along the z axis) generate the infinite lattice. Figure 2 is a sketch of the structure of the twin-plane arrangement. The twin planes repeat at a distance that is determined by the variable size of the supercell. The static crystal is treated within the framework of a Born-type model [12]. Silver and halide ions are treated by the shell model [13], which allows for polarization and thus incorporates the dielectric properties of the crystal. The short-range interactions between ions are treated by two-body
(4) interactions, where rij is the distance between ions and A, p, and C are constants of the potential. Three-body
terms take the form C( 1 + 3 COS hjk
=
0i COS Oj COS ok)
R!R!R3 1 I
(5) k
where the sides and angles of a triangle formed by ions i, j, and k are represented by R and 0, respectively, and C is a constant of the potential. In the crystal calculation, the ions relax to an equilibrium position. This is achieved through
TWIN PLANE
-
TWIN PLANE
-
TWINPLANE
///////
TWIN PLANE
Fig. 2. Sketchofa segment of the infinite lattice model used to represent twin planes.
Computations of properties of twin planes in silver halide reducing the force on each ion to zero. At this geometry, the Madelung potential at each site may be computed by
where z is the charge, R is the distance, and e is the electron unit charge with the familiar lattice sum. This sum contains long-range terms, so Ewald-type approaches [14] are used to evaluate it. Several potentials for the silver halides have been developed by Jacobs, Catlow, and coworkers [ 15, 161. First there is the strictly two-body form. Such potentials have proven useful [8, 17- 191for studies of point defects, surfaces, and impurities in silver chloride and bromide. Their principal deficiencies are the prediction of elastic constants where Cl2 = C,, low silver ion diffusion mobilities, and poor phonon spectra. The three-body potentials get the elastic constants correct and improve the ion mobility, but still fail to get good phonon spectra [ 16,201. Work is underway to improve this situation [21]. The properties we will be studying at the twin planes have been treated well by the two- and three-body potentials. Thus, while future developments may lead to improved potentials, there is no reason to believe that our results will be significantly changed by the new potentials. The two- and three-body potentials employed in this work are taken directly from Refs [15] and [16], and not repeated here. The designation CCHJ X refers to potentials from Ref. [15]. The three-body potentials are of the triple-dipole type from Ref. [16]. The interaction of an Ago atom with lattice ions was calculated by unrestricted Hartree-Fock with MP2 correlation effects. The interaction is calculated using an ion, such as Ag’, Cl-, or Br-, embedded within a neutral hemispherical array of integer point charges positioned at silver halide sites. The quantum mechanical ion is positioned at the center of the flat side of the hemisphere. The Ago atom is positioned on top of this ion and the energy is calculated as the distance is varied. The interaction energy between the two are fit to eqn (4) to give the parameters in Table 1. We employ double-zeta plus polarization functions for Table 1. Two-body interatomic potentials for silver atom with lattice ions computed by UHF with MP2 correlation energy Interactiont
A (eV)
P (A)
Ago-Ag+ Ai’-& Ago-BY
11387.3 9258.4 10619.1
0.28050 0.27911 0.28735
C (eV - A6)
389.3 371.3 526.8 tCutoff distance employed in simulations was 1.5 times nearest-neighbor distance.
629
halide ions and a pseudo-potential with double-zeta plus polarization valence basis functions on silver atoms. There are approximations inherent in our approach that will be mentioned. One is that we use the formal charges of fl for silver and halide ions. While silver chloride and bromide have a Phillips ionicity of 0.86 and 0.85, respectively, and the sixfold coordination of ionic crystals, they cannot be viewed as fully ionic. Nevertheless, a realistic lattice energy for these materials can only be computed if the formal charges are used. Likewise, very accurate dielectric and elastic properties of silver halide are computed within this model [ 15, 161.Thus, for many properties, this model is an appropriate representation for silver halide. Isolated defects, such as ionic point defects, trapped electrons, or holes are treated within a Mott-Littleton, two-region framework. The ions surrounding the defect, up to approximately eight nearest-neighbor distances in radius, are treated explicitly. The remaining ions are treated within the framework of a continuum theory. The two regions are interfaced appropriately. The computer code CASCADE [14] is employed for this calculation. In a defect calculation, the ions in the inner region are allowed to polarize so that the force on each species is zero. An iterative procedure is required to achieve this equilibrium geometry. The energy corresponding to this geometry is then computed. We note that in silver halide, and most ionic crystals, the lattice polarization effects extend several atomic radii beyond a charged defect. 3. RESULTS We begin by considering the energy required to form a twin plane relative to the perfect crystal. We compute the difference in lattice energies for the perfect and twin-plane configurations. Recall that the lattice energy is the energy released on taking one anion and cation from infinity to the crystal. We divide the difference in lattice energies by the area of the basis (since the twin plane is a two-dimensional defect) to obtain the values shown in Table 2. We first consider formation energies for AgCl twin planes as a function of their separation. The energies are constant as the twin-plane separation is varied, indicating no direct interaction between planes for separations of 19A or greater. The values of the formation energy depend upon the interatomic potentials used in the calculation, but each predicts that the chloride twin plane forms more easily than the silver twin plane. The values calculated with the two-body potentials are thought to be more realistic because the bond angles at the twin plane deviate considerably from those
630
R. C. BAETZOLD
Table 2. The energy required to form twin planes versus perfect crystal Twin
Separation (A)t
A E (J/m*)
AgCl CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III Three-body Three-body
A8 A8 A8 A8 CI Cl Cl CI A8 Cl Ag Cl
19 29 48 86 19 29 48 86 86 86 86 86
0.232 0.232 0.232 0.232 0.200 0.200 0.200 0.191 0.243 0.191 0.682 0.018
AgBr CCHJ II CCHJ II Three-body Three-body
A8 Br Ag Br
89 89 89 89
0.264 0.176 0.858 0.126
Potential
TSeparation of the twin planes. in the perfect crystal, where the parameters for the three-body potential were determined. In the case of AgBr, the halide twin plane forms significantly more easily than the silver twin plane. As mentioned earlier, ions must relax to accommodate the strains induced by the presence of the twin plane. These relaxations are observed principally in the two planes of ions adjacent to the twin plane. These ions move in a direction normal to the twin plane. For AgBr, the Ag+ ions move 0.03 A away from the Br- twin plane and the Br- ions move 0.09 A away from the Agf twin plane. For AgCl, the Ag+ ions move 0.01 A away from the Cl- twin plane and the Cl- ions move 0.07 A away from the Ag+ twin plane. These distances are relative to the separation of {111) planes in the perfect crystal. The distances between planes further away from the twin planes are practically unperturbed from their perfect crystal values. It is expected that the magnitudes of these relaxation effects would be difficult to detect experimentally. Now we consider the Madelung potential computed at ion sites within various planes in crystals containing a twin plane. First, we sketch the behavior of this potential in Fig. 3 for different situations. In the perfect crystal, the potential at the cation is repulsive (moved towards vacuum) caused by the dominant Coulombic effect of the six nearest-neighbor anions. The reverse situation is true for the potential at the anion sites. The magnitude of the potential is the same for all bulk anions or all bulk cations. Now consider twin planes in sections (b) and (c) of the figure. The potential is decreased in absolute value at the twin plane and to a smaller extent at the two planes adjacent. At greater distances the absolute value of the potential becomes bulk-like. The actual values
(4
l L-r-!-!-__r I r-l r-l t-l “P Ad
X-
As+
X‘
Ag+
X-
(b) I
(-l-J&Jl
Fig. 3. Sketch of the Madelung potential in a direction normal to the {111) plane as alternate planes are intersected. The perfect crystal is considered in (a), the Ag+ twin plane in (b), and the halide twin plane in (c). Note the decrease in amplitude of the potential at the twin plane. computed for AgCl and AgBr, using several potentials, are shown in Table 3. It is interesting to examine the shift in potential from bulk to the twin planes. At Ag+ twin planes the magnitude of the shift is 0.4-0.5 V for both AgCl and AgBr. At halide twin planes the magnitude of the shift is O.l-0.2V. The range of this effect is only one or two planes. These shifts indicate that at a Ag+ twin plane, the potential is 0.4-0.5 V more stable for an electron, while at a halide twin plane, the potential is 0.1-0.2 V more stable for a hole, depending upon the halide type. As a result of the variations in Madelung potential at the twin plane, it is expected that localized defects might have formation energies different than in the perfect crystal. We performed calculations within the Mott-Littleton framework in order to investigate this possibility. We have considered formation of atoms of silver or halogen and silver ion vacancies and interstitials next to the twin plane. We begin with AgBr calculations with the CCHJ II potential in Table 4. We consider the energy of substituting a silver atom for a silver ion as a function of distance from the twin plane. This step requires energy and the smallest value occurs right on a silver ion twin plane. It is roughly 0.05 eV easier to form a silver atom at this site than at another silver ion site in the perfect crystal. This preferential energy is considerably less than the 0.4V difference in Madelung potential at these two sites and apparently reflects factors due to lattice polarization. A localized Bra atom forms roughly 0.1 eV more easily near the Agf twin plane than in the bulk. Both Ag’ vacancies
631
Computations of properties of twin planes in silver halide Table 3. Madelung potential versus distance from twin plane AgCl
AgBr Plane
Distance?
CCHJ II potential (V)
Three-body potential (V)
CCHJ III potential (V)
Three-body potential (V)
8.339 -8.676 8.752 -8.736 8.753 -8.737 8.753
8.318 -8.726 8.834 -8.808 8.828 -8.811 8.828
8.814 -9.070 9.155 -9.143 9.157 -9.144 9.157
8.660 -9.067 9.154 -9.128 9.150 -9.131 9.149
-8.526 8.712 -8.740 8.736 -8.749 8.736 -8.749
-8.639 8.796 -8.816 8.815 -8.826 8.814 -8.826
-8.892 9.115 -9.144 9.141 -9.155 9.141 -9.155
-9.072 9.081 -9.138 9.136 -9.145 9.135 -9.145
Ag’ twin 0
$;
a/& 2a/& 3a/J5 4a/v0 5a/v? 6a/&
Ag+ XAg+ XAg+ X- twin X_ Ag+ XAg+ XAg+ X-
0 a/J5
2a/& 3a/J5 da/J5
5a/\/5 6a/fi
tDistance normal from the twin plane. IX- denotes a Cl- or Br- ion.
and interstitials form more easily near the Agf twin plane. Near the Br twin plane these effects are changed somewhat. It is slightly more difficult to form an Ago near the Br- twin plane than in the bulk. The Bra hole is almost 0.2eV more stable on the Br- twin plane than in the bulk. There is only a small effect on the vacancy energy of formation caused by the Br- twin plane. Note that electron affinity values are not included in the Ago and Bra formation terms, but should be added to complete possible thermodynamic cycles.
Computations for AgCl using the CCHJ III potentials give very similar effects to AgBr. Table 5 contains these results. The Agf twin plane is a preferable site for Ago formation. Localized holes such as Cl0 can form more easily at the Cl- or next to the Ag+ twin planes than in the bulk. Both components of the Frenkel defect pair can form more easily at the twin plane than in the bulk. We may consider whether divalent impurities would segregate to twin planes. Such an effect might be possible because of the changes in Madelung potential
Table 4. Energy to form localized defects in AgBr
Plane
Distance
Ag+ twin plane Ag+ 0 Bra/J5 2alJ5 Ag+ Br3alJ5 Ag+
4a/JS
BrAg+ Br-
5a/& 6a/& 7a/&
Br- twin plane Br0 a/J5 Ag+ Br2a/JS 3alv5 Ag+ Br4alJ5 5a/JS Ag+ Br6alfi 7afJ5 Ag+ tThe energy change $The energy change §The energy change T[Theenergy change
Substitute? Ago for Ag+ (eV)
Substitutet
Agf vacancy5
Ag+ interstitial7
Bra for Br- (eV)
formation (eV)
formation (eV)
5.058
-4.151
5.298
-3.901
5.319
-3.942
5.323
-3.931
1.564 4.876 1.636 4.964 1.614 4.973 1.616 4.973
4.793
5.283
4.956
5.305
4.985
5.308
4.986
5.309
1.627
-4.1 IO -3.951
1.606
-3.945
1.604 1.605 to take an electron from infinity to the ion. to take a hole from infinity to the ion. to remove an ion to infinity. to move an ion from infinity to the crystal next to the twin plane.
-3.949
R. C. BAETZOLD
632
Table 5. Energy to form localized defects in AgCl Plane
Distance
Ag+ twin plane Ag+ 0 Cla/d Ag+ 2alfi
clA8+ ClA8+ Cl-
Substitute Ago for Ag+ (eV)
Substitute Cl0 for Cl- (eV)
1.591
Ag+ interstitial formation (eV)
5.438
-4.041
5.643
-3.700
5.664
-3.689
5.667
-3.679
5.147
1.692 5.350
3ald
4al\/j 5a/fi
1.654
halfi 7alJ5
1.654
Cl- twin plane Cl0 Ag+ al& Cl2al& 3a/fi Ag+ Cl4alJj Ag+ 5a/& Cl6a/fi Ag+ 7JJ5
5.359 5.360
5.371
5.653 -3.709
1.716
Cl- twin plane - 10.362 aI& - 10.260 3alJ5
-9.163 -9.03 1
-8.045 -7.888
-9.023 -9.023
-7.880 -7.879
10.252
5.652 -3.713
-7.921 -7.954 -7.892 -7.888
-
5.370 1.716
-8.981 -9.090 -9.037 -9.034
- 10.252
5.648 -3.805
Pb*+
7ald
5.338 1.720
Cd*+
544
5.610 -3.999
Ag+ twin plane 0 -10.106 -10.315 2ald3 - 10.268 4alJ5 - 10.265 6alfi
Zn*+
5.150 1.721
Table 6. Energy (eV) of impurity substitution for Agf versus distance from the twin plane in AgCl Distance
Ag+ vacancy formation (eV)
This type of double twin plane might have an important influence on hole, but not electron properties. 4. DISCUSSION
near the twin planes. Table 6 shows the energy of substitution of Zn*+, Cd*+, and Pb*+ impurities for Ag+ ions computed at various positions relative to the twin planes. At the Ag+ twin plane in AgCl, there is a small preference for Pb*+ to segregate near the twin plane, but this is not true for Zn*+ and Cd*+. Near the Cl- twin plane, there is an energetic preference for all of these ions to segregate. It is difficult to make any generalization based on these results because several effects, including size of the impurity, the distortions near the twin plane, and the variations in potential might be operating here. Defects near the double twin plane described in eqn (3) have been studied. For AgCl, using the CCHJ III potential, the energy of formation of this stacking arrangement is 0.404 J/m*, which is approximately two times larger than the comparable twin plane energies of formation in Table 2. Thus, this ‘double’ stacking fault is considerably less likely than the twinplane arrangement. Formation energies of Ago in the double twin region are about the same as the bulk, so there is no preference for Ago. There is a preference for Cl0 formation in this region by 0.3 eV versus the bulk.
We have found that energy is required to form twin planes relative to the perfect crystal. The formation energy per unit area is roughly comparable for Cland Ag+ twin planes in AgCl, but smaller for Br than Ag+ twin planes in AgBr. These formation energies may be compared with corresponding values in other materials. In NaCl { 11I} stacking fault energies are calculated [22] to range from 0.24 to 0.81 J/m’ versus our computed twin-plane energies of 0.23 J/m* for AgCl and 0.18 J/m* for AgBr. Other alkali halide stacking fault energies are a few times larger for Li salts with small halide ions and smaller for Rb salts with larger halide ions. There are no experimental data available for comparison. The surface energy of {ill} AgBr was previously [8] calculated to be 0.58 J/m*, which seems to be reasonable relative to the twin-plane energy, because the surface is a much more drastic discontinuity. Comparison of the difference in lattice energy of a supercell containing one twin plane to the lattice energy of a supercell of perfect silver halide gives a value of approximately 1% of the crystal energy, indicating the rather small formation energy of this stacking fault. Summing up, our comparisons of stacking fault energies of twin planes to other calculations are reasonable, but there are no good experimental data for comparison. One may ask how twin planes grow during solution deposition on {11 I} surfaces. Of course, the exact structure of the {Ill} surface is poorly defined, although some models [8, 231 have been advanced. In any case, the top surface, while incomplete,
Computations of properties of twin planes in silver halide contains ions of all one type. Growth of a second layer on this surface probably proceeds in a layer-by-layer mode. When the incoming ions bind to a site, they are in equilibrium with the liquid phase so that reversible adsorption-desorption is occurring. Once an ion has remained on the surface sufficiently long enough for subsequent ions to bind around it, a patch of ions is created with the { 111) registry. Thus, all that is required to start this process is that the starting ion bind in the wrong hollow site (i.e. the site leading to twin planes). We note that earlier calculations [8] have shown that the hollow site is the preferred binding site for adions, as expected from general considerations of their closed-shell, spherical nature. This overall mechanism seems to be a likely mode of formation of twin planes. Steps that lead to slower growth should reduce the occurrence of twin planes if this mechanism is right. The calculations predict that Br- twin planes would be predominant in AgBr, because Ag+ twin planes have somewhat larger formation energies. The difference in formation energy, however, is of small enough magnitude so that both types of twin planes could be formed. For AgCl, the differences are even smaller and it is likely that both planes could coexist. Indeed, models containing a jog on the twin plane have been proposed [9] that would possess both types of twin plane. The Madelung potentials clearly indicate deeper levels for electrons at Ag’ twin planes than the bulk of AgCl or AgBr. Holes have a potential of about 0.2eV more favorable for trapping at halide twin planes than bulk in both AgCl and AgBr. The range of these effects is very small, extending less than one lattice constant normal to the twin plane. These effects might reduce transport of photocarriers across the twin plane interface. This indirect deduction concerning the effect of twin planes upon carrier mobility depends upon the delocalized character of the carrier. We estimate that the trap depth of a 258 radius polaron is only a few meV based upon the weighted volume fraction of the twin plane. Such delocalized species should experience only a minor perturbation due to the twin plane. On the other hand, a Ago atom would have a trap depth of a few tenths of an eV. Thus, the effect of the twin plane on mobility depends strongly on the size of the carrier. Localized defects such as Ago or Bra show a preference for location on or near twin planes in accord with the Madelung potential considerations just discussed. The magnitude of the effect is reduced, though, because of the strong interaction with the lattice. Ionic point defects have lower formation energies near the twin plane. This probably arises because of the lattice distortions in this region of the
633
crystal. This effect is true for both silver ion vacancies and interstitials, so it is unlike a space charge layer. An effective reduction of about 0.4eV in Frenkel defect energy is computed in AgCl and AgBr, so that there could be a significant increase in concentration of both point defects right near the twin plane as compared to the bulk. One proposal [6] that was advanced earlier for twin planes is that interstitial silver ions adjacent to the twin plane could be easily reduced to Ago in this region of structural disorder. We have examined this effect computationally for AgCl by determining the energy required to convert an interstitial silver ion to an atom. The only significant effect is at the silver ion twin plane, where the required energy is 1.14eV compared to the corresponding value 1.80eV in the bulk. This value is also significantly less than energies for conversion of Ag+ to Ago at a lattice site, as shown in Table 5. Thus, the Ag+ twin plane could act to concentrate both electrons and interstitial silver ions leading to Ago formation. It is interesting that this mechanism operates without a partial charge, as is invoked for surface [24] mechanisms of latent image formation involving defects such as kinks.
5. CONCLUSIONS This report has involved a first attempt to calculate the electronic properties of twin planes in silver halide. It has shown that there are significant differences in the hole and electron trapping properties of silver or halide twin planes. Based on energy differences that are small, both types of twin planes seem possible, but the halide form is most stable. The silver twin plane has a Madelung potential reduced from bulk values by 0.4-0.5V, which accounts for its enhanced electron trapping properties. Support is given for a proposal suggesting easier reduction of interstitial silver ions to atoms in the presence of a silver ion twin plane. Acknowledgements-1 am grateful to Al Marchetti, Ken Lushington, Ray Eachus, and Sam Chen for valuable discussions.
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Imag. Sci. Technol. 37,107 (1993) and references therein. 6. Hamilton J. F., Photogr. Sci. Engng 11, 57 (1967).
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I. Hamilton J. F., Phifos. Mug. 16, 1 (1967). 8. Baetzold R. C., Tan Y. T. and Tasker P. W., Surf. Sci.
195,579 (1988). 9. Sprackling M. T., J. Photogr. Sci. 32,21 (1984). 10. Hamilton J. F. and Brady L. E., .r. Appl. Phys. 35,414 (1964).
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Pergamon
COMPUTATIONS
.I Phys. Chem Solids Vol57. No 5, pp. 627-634.1996 Copyright 0 1996 Eastman Kodak Company. Published by Elswier Science Ltd Printed in Great Britain. All nghts reserved 0022-3697196 $15 00 + 0.00
OF PROPERTIES OF TWIN IN SILVER HALIDE
PLANES
ROGER C. BAETZOLD Imaging Research and Advanced Development, Eastman Kodak Company, Rochester, NY 14650, U.S.A (Received 2 April 1995; accepted 11 July 1995)
Abstract-Computer simulations have been applied to treat the defect properties influenced by twin planes in silver halide. The formation energy of silver and halide twin planes is roughly equal in AgCI, but halide is significantly smaller in AgBr. The Madelung potential is attenuated at twin planes, promoting electron trapping at silver and hole trapping at halide twin planes. The formation energy of components of the Frenkel defect is reduced at the twin plane relative to the perfect crystal. Keywords:
A. inorganic compounds, A. semiconductors, D. crystal structure, D. defects.
1. INTRODUCTION
by
Twin planes are present in most tabular silver halide
grains. They have been observed experimentally [l-3] through various diffraction experiments and detected in transmission electron microscopy (TEM) crosssection experiments [4]. In fact, the growth of tabular grains has been explained through models [S] that require the presence of twin planes. These models consider that, because of special properties of the sites where twin planes intersect the surface, there will be preferential deposition of ions from solution as compared to sites on flat surfaces. Frequently, a doubly twinned plane is present in grains as observed in electron diffraction [6,7]. This structure can grow in a self-perpetuating manner. Owing to the ubiquitous presence of twin planes, one can contemplate their possible role in the photographic effect. So far, a complete understanding of this role is lacking. Consider specifically how {111) layers of a rock salt structure such as silver halide assemble. Any { 111) layer is composed of ions of all the same type and having a spacing of &a, where a is the nearestneighbor distance. The ions in this layer are positioned to form equilateral triangles on sites we shall designate as A, as shown in Fig. 1. Now ions of the opposite charge forming adjacent layers may bind at various sites above this layer. For ionic binding, the hollow sites are preferred [8], and are designated B or C in Fig. 1. Once either choice is made, additional ions are deposited in registry to complete this {111) layer. Ions for the third layer alternate again in sign and deposit at the B or C site unoccupied by the second layer, or the A site [9]. The perfect fee rock salt crystal structure has a site occupancy on {111) layers given
ABCABCABC
(1)
Now consider the site occupancy taken at a twin plane. Here, we begin by the normal ABC sequence, but then the next layer occupies a B site rather than the expected A site and the growth sequence now becomes BAC. ABCABCBACBAC
(2)
such that the C layer becomes the twin plane and there is reflection symmetry across this twin plane, referred to as a stacking fault. We may also note another potential type of stacking fault. Suppose that after the B sites are occupied, the original growth sequence of ABC is retained. This results in the pattern ABCABCBCABCABC
(3)
This stacking fault has two adjacent layers with an incorrect placement of ions (BCB) and (CBC). One should expect this stacking fault to have roughly twice the energy of formation of the twin plane, since the surface area containing the defect is doubled and therefore, less probable. Let us consider how the presence of twin planes changes the interactions in a crystal. Because it is the next-nearest neighbors that have a changed relative placement due to the twin planes, we expect the perturbations to be short ranged. In the perfect crystal, the distance between next-nearest neighbors is &a versus 2a/fi at the twin plane, as sketched in Fig. l(b). The next-nearest neighbor ions have the 627
R. C. BAETZOLD
628
m
A
(a)
0.
.c
(W
:
2. METHOD
:
I
I
I
I I
d
d
I
PERFECT
impurity segregation, or point defect properties. Finally, we note that two types of twin planes are possible as characterized by whether a halide or silver ion is on the twin plane.
TWIN PLANE
Fig. 1. A segment of the {111) layer of a silver halide plane is shown with ions at sites designated A. The sites B or C in the center of equilateral triangles are available for growth of the next layer. In (b) the next-nearest neighbor positions denoted X are shown for perfect and twin planes. same charge. In the unrelaxed crystal, these ions are positioned 18% closer. This distortion will cause a significant change in the interatomic interaction that is based on electrostatic, polarization, and short-range terms. The crystal will be forced to relax in this region to achieve a zero force structure. Also, because the interatomic terms differ for silver and halide ions, the properties of silver and halide ion twin planes will be different. Photolysis of unsensitized silver bromide grains often leads to silver formation at twin planes. This has been revealed experimentally using electron microscopy to study protrusions on a heavily exposed grain [lo]. These experiments imply some special electronic properties for twin planes that influence photocarriers or facilitate the growth of silver. However, because the exposure levels are much greater than those employed in typical photographic experiments, it is unclear whether the twin planes are important in the latter process. On the other hand, experiments [l l] at lower light exposures have given evidence for formation of photolytic silver and were interpreted to indicate effective electron trapping sites along the twin plane. The purpose of this report is to provide some initial studies of the structure and electronic properties of twin planes in silver halide. It has not been clear whether twin planes should introduce any electronic perturbation that would significantly effect electronic or ionic defects. There are other questions that arise concerning the geometric distortions at a twin plane and whether the possible strain introduced into a crystal would change carrier trapping properties,
The method employed in these calculations to simulate twin planes involves constructing a supercell within a three-dimensional infinite representation. The large cell contains a chain of ions placed according to eqn (2). The translation vectors (a, O,O)a, (l/a, fl, 0) a, and (0,0,z) a (where z is the repeat distance on the chain along the z axis) generate the infinite lattice. Figure 2 is a sketch of the structure of the twin-plane arrangement. The twin planes repeat at a distance that is determined by the variable size of the supercell. The static crystal is treated within the framework of a Born-type model [12]. Silver and halide ions are treated by the shell model [13], which allows for polarization and thus incorporates the dielectric properties of the crystal. The short-range interactions between ions are treated by two-body
(4) interactions, where rij is the distance between ions and A, p, and C are constants of the potential. Three-body
terms take the form C( 1 + 3 COS hjk
=
0i COS Oj COS ok)
R!R!R3 1 I
(5) k
where the sides and angles of a triangle formed by ions i, j, and k are represented by R and 0, respectively, and C is a constant of the potential. In the crystal calculation, the ions relax to an equilibrium position. This is achieved through
TWIN PLANE
-
TWIN PLANE
-
TWINPLANE
///////
TWIN PLANE
Fig. 2. Sketchofa segment of the infinite lattice model used to represent twin planes.
Computations of properties of twin planes in silver halide reducing the force on each ion to zero. At this geometry, the Madelung potential at each site may be computed by
where z is the charge, R is the distance, and e is the electron unit charge with the familiar lattice sum. This sum contains long-range terms, so Ewald-type approaches [14] are used to evaluate it. Several potentials for the silver halides have been developed by Jacobs, Catlow, and coworkers [ 15, 161. First there is the strictly two-body form. Such potentials have proven useful [8, 17- 191for studies of point defects, surfaces, and impurities in silver chloride and bromide. Their principal deficiencies are the prediction of elastic constants where Cl2 = C,, low silver ion diffusion mobilities, and poor phonon spectra. The three-body potentials get the elastic constants correct and improve the ion mobility, but still fail to get good phonon spectra [ 16,201. Work is underway to improve this situation [21]. The properties we will be studying at the twin planes have been treated well by the two- and three-body potentials. Thus, while future developments may lead to improved potentials, there is no reason to believe that our results will be significantly changed by the new potentials. The two- and three-body potentials employed in this work are taken directly from Refs [15] and [16], and not repeated here. The designation CCHJ X refers to potentials from Ref. [15]. The three-body potentials are of the triple-dipole type from Ref. [16]. The interaction of an Ago atom with lattice ions was calculated by unrestricted Hartree-Fock with MP2 correlation effects. The interaction is calculated using an ion, such as Ag’, Cl-, or Br-, embedded within a neutral hemispherical array of integer point charges positioned at silver halide sites. The quantum mechanical ion is positioned at the center of the flat side of the hemisphere. The Ago atom is positioned on top of this ion and the energy is calculated as the distance is varied. The interaction energy between the two are fit to eqn (4) to give the parameters in Table 1. We employ double-zeta plus polarization functions for Table 1. Two-body interatomic potentials for silver atom with lattice ions computed by UHF with MP2 correlation energy Interactiont
A (eV)
P (A)
Ago-Ag+ Ai’-& Ago-BY
11387.3 9258.4 10619.1
0.28050 0.27911 0.28735
C (eV - A6)
389.3 371.3 526.8 tCutoff distance employed in simulations was 1.5 times nearest-neighbor distance.
629
halide ions and a pseudo-potential with double-zeta plus polarization valence basis functions on silver atoms. There are approximations inherent in our approach that will be mentioned. One is that we use the formal charges of fl for silver and halide ions. While silver chloride and bromide have a Phillips ionicity of 0.86 and 0.85, respectively, and the sixfold coordination of ionic crystals, they cannot be viewed as fully ionic. Nevertheless, a realistic lattice energy for these materials can only be computed if the formal charges are used. Likewise, very accurate dielectric and elastic properties of silver halide are computed within this model [ 15, 161.Thus, for many properties, this model is an appropriate representation for silver halide. Isolated defects, such as ionic point defects, trapped electrons, or holes are treated within a Mott-Littleton, two-region framework. The ions surrounding the defect, up to approximately eight nearest-neighbor distances in radius, are treated explicitly. The remaining ions are treated within the framework of a continuum theory. The two regions are interfaced appropriately. The computer code CASCADE [14] is employed for this calculation. In a defect calculation, the ions in the inner region are allowed to polarize so that the force on each species is zero. An iterative procedure is required to achieve this equilibrium geometry. The energy corresponding to this geometry is then computed. We note that in silver halide, and most ionic crystals, the lattice polarization effects extend several atomic radii beyond a charged defect. 3. RESULTS We begin by considering the energy required to form a twin plane relative to the perfect crystal. We compute the difference in lattice energies for the perfect and twin-plane configurations. Recall that the lattice energy is the energy released on taking one anion and cation from infinity to the crystal. We divide the difference in lattice energies by the area of the basis (since the twin plane is a two-dimensional defect) to obtain the values shown in Table 2. We first consider formation energies for AgCl twin planes as a function of their separation. The energies are constant as the twin-plane separation is varied, indicating no direct interaction between planes for separations of 19A or greater. The values of the formation energy depend upon the interatomic potentials used in the calculation, but each predicts that the chloride twin plane forms more easily than the silver twin plane. The values calculated with the two-body potentials are thought to be more realistic because the bond angles at the twin plane deviate considerably from those
630
R. C. BAETZOLD
Table 2. The energy required to form twin planes versus perfect crystal Twin
Separation (A)t
A E (J/m*)
AgCl CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III CCHJ III Three-body Three-body
A8 A8 A8 A8 CI Cl Cl CI A8 Cl Ag Cl
19 29 48 86 19 29 48 86 86 86 86 86
0.232 0.232 0.232 0.232 0.200 0.200 0.200 0.191 0.243 0.191 0.682 0.018
AgBr CCHJ II CCHJ II Three-body Three-body
A8 Br Ag Br
89 89 89 89
0.264 0.176 0.858 0.126
Potential
TSeparation of the twin planes. in the perfect crystal, where the parameters for the three-body potential were determined. In the case of AgBr, the halide twin plane forms significantly more easily than the silver twin plane. As mentioned earlier, ions must relax to accommodate the strains induced by the presence of the twin plane. These relaxations are observed principally in the two planes of ions adjacent to the twin plane. These ions move in a direction normal to the twin plane. For AgBr, the Ag+ ions move 0.03 A away from the Br- twin plane and the Br- ions move 0.09 A away from the Agf twin plane. For AgCl, the Ag+ ions move 0.01 A away from the Cl- twin plane and the Cl- ions move 0.07 A away from the Ag+ twin plane. These distances are relative to the separation of {111) planes in the perfect crystal. The distances between planes further away from the twin planes are practically unperturbed from their perfect crystal values. It is expected that the magnitudes of these relaxation effects would be difficult to detect experimentally. Now we consider the Madelung potential computed at ion sites within various planes in crystals containing a twin plane. First, we sketch the behavior of this potential in Fig. 3 for different situations. In the perfect crystal, the potential at the cation is repulsive (moved towards vacuum) caused by the dominant Coulombic effect of the six nearest-neighbor anions. The reverse situation is true for the potential at the anion sites. The magnitude of the potential is the same for all bulk anions or all bulk cations. Now consider twin planes in sections (b) and (c) of the figure. The potential is decreased in absolute value at the twin plane and to a smaller extent at the two planes adjacent. At greater distances the absolute value of the potential becomes bulk-like. The actual values
(4
l L-r-!-!-__r I r-l r-l t-l “P Ad
X-
As+
X‘
Ag+
X-
(b) I
(-l-J&Jl
Fig. 3. Sketch of the Madelung potential in a direction normal to the {111) plane as alternate planes are intersected. The perfect crystal is considered in (a), the Ag+ twin plane in (b), and the halide twin plane in (c). Note the decrease in amplitude of the potential at the twin plane. computed for AgCl and AgBr, using several potentials, are shown in Table 3. It is interesting to examine the shift in potential from bulk to the twin planes. At Ag+ twin planes the magnitude of the shift is 0.4-0.5 V for both AgCl and AgBr. At halide twin planes the magnitude of the shift is O.l-0.2V. The range of this effect is only one or two planes. These shifts indicate that at a Ag+ twin plane, the potential is 0.4-0.5 V more stable for an electron, while at a halide twin plane, the potential is 0.1-0.2 V more stable for a hole, depending upon the halide type. As a result of the variations in Madelung potential at the twin plane, it is expected that localized defects might have formation energies different than in the perfect crystal. We performed calculations within the Mott-Littleton framework in order to investigate this possibility. We have considered formation of atoms of silver or halogen and silver ion vacancies and interstitials next to the twin plane. We begin with AgBr calculations with the CCHJ II potential in Table 4. We consider the energy of substituting a silver atom for a silver ion as a function of distance from the twin plane. This step requires energy and the smallest value occurs right on a silver ion twin plane. It is roughly 0.05 eV easier to form a silver atom at this site than at another silver ion site in the perfect crystal. This preferential energy is considerably less than the 0.4V difference in Madelung potential at these two sites and apparently reflects factors due to lattice polarization. A localized Bra atom forms roughly 0.1 eV more easily near the Agf twin plane than in the bulk. Both Ag’ vacancies
631
Computations of properties of twin planes in silver halide Table 3. Madelung potential versus distance from twin plane AgCl
AgBr Plane
Distance?
CCHJ II potential (V)
Three-body potential (V)
CCHJ III potential (V)
Three-body potential (V)
8.339 -8.676 8.752 -8.736 8.753 -8.737 8.753
8.318 -8.726 8.834 -8.808 8.828 -8.811 8.828
8.814 -9.070 9.155 -9.143 9.157 -9.144 9.157
8.660 -9.067 9.154 -9.128 9.150 -9.131 9.149
-8.526 8.712 -8.740 8.736 -8.749 8.736 -8.749
-8.639 8.796 -8.816 8.815 -8.826 8.814 -8.826
-8.892 9.115 -9.144 9.141 -9.155 9.141 -9.155
-9.072 9.081 -9.138 9.136 -9.145 9.135 -9.145
Ag’ twin 0
$;
a/& 2a/& 3a/J5 4a/v0 5a/v? 6a/&
Ag+ XAg+ XAg+ X- twin X_ Ag+ XAg+ XAg+ X-
0 a/J5
2a/& 3a/J5 da/J5
5a/\/5 6a/fi
tDistance normal from the twin plane. IX- denotes a Cl- or Br- ion.
and interstitials form more easily near the Agf twin plane. Near the Br twin plane these effects are changed somewhat. It is slightly more difficult to form an Ago near the Br- twin plane than in the bulk. The Bra hole is almost 0.2eV more stable on the Br- twin plane than in the bulk. There is only a small effect on the vacancy energy of formation caused by the Br- twin plane. Note that electron affinity values are not included in the Ago and Bra formation terms, but should be added to complete possible thermodynamic cycles.
Computations for AgCl using the CCHJ III potentials give very similar effects to AgBr. Table 5 contains these results. The Agf twin plane is a preferable site for Ago formation. Localized holes such as Cl0 can form more easily at the Cl- or next to the Ag+ twin planes than in the bulk. Both components of the Frenkel defect pair can form more easily at the twin plane than in the bulk. We may consider whether divalent impurities would segregate to twin planes. Such an effect might be possible because of the changes in Madelung potential
Table 4. Energy to form localized defects in AgBr
Plane
Distance
Ag+ twin plane Ag+ 0 Bra/J5 2alJ5 Ag+ Br3alJ5 Ag+
4a/JS
BrAg+ Br-
5a/& 6a/& 7a/&
Br- twin plane Br0 a/J5 Ag+ Br2a/JS 3alv5 Ag+ Br4alJ5 5a/JS Ag+ Br6alfi 7afJ5 Ag+ tThe energy change $The energy change §The energy change T[Theenergy change
Substitute? Ago for Ag+ (eV)
Substitutet
Agf vacancy5
Ag+ interstitial7
Bra for Br- (eV)
formation (eV)
formation (eV)
5.058
-4.151
5.298
-3.901
5.319
-3.942
5.323
-3.931
1.564 4.876 1.636 4.964 1.614 4.973 1.616 4.973
4.793
5.283
4.956
5.305
4.985
5.308
4.986
5.309
1.627
-4.1 IO -3.951
1.606
-3.945
1.604 1.605 to take an electron from infinity to the ion. to take a hole from infinity to the ion. to remove an ion to infinity. to move an ion from infinity to the crystal next to the twin plane.
-3.949
R. C. BAETZOLD
632
Table 5. Energy to form localized defects in AgCl Plane
Distance
Ag+ twin plane Ag+ 0 Cla/d Ag+ 2alfi
clA8+ ClA8+ Cl-
Substitute Ago for Ag+ (eV)
Substitute Cl0 for Cl- (eV)
1.591
Ag+ interstitial formation (eV)
5.438
-4.041
5.643
-3.700
5.664
-3.689
5.667
-3.679
5.147
1.692 5.350
3ald
4al\/j 5a/fi
1.654
halfi 7alJ5
1.654
Cl- twin plane Cl0 Ag+ al& Cl2al& 3a/fi Ag+ Cl4alJj Ag+ 5a/& Cl6a/fi Ag+ 7JJ5
5.359 5.360
5.371
5.653 -3.709
1.716
Cl- twin plane - 10.362 aI& - 10.260 3alJ5
-9.163 -9.03 1
-8.045 -7.888
-9.023 -9.023
-7.880 -7.879
10.252
5.652 -3.713
-7.921 -7.954 -7.892 -7.888
-
5.370 1.716
-8.981 -9.090 -9.037 -9.034
- 10.252
5.648 -3.805
Pb*+
7ald
5.338 1.720
Cd*+
544
5.610 -3.999
Ag+ twin plane 0 -10.106 -10.315 2ald3 - 10.268 4alJ5 - 10.265 6alfi
Zn*+
5.150 1.721
Table 6. Energy (eV) of impurity substitution for Agf versus distance from the twin plane in AgCl Distance
Ag+ vacancy formation (eV)
This type of double twin plane might have an important influence on hole, but not electron properties. 4. DISCUSSION
near the twin planes. Table 6 shows the energy of substitution of Zn*+, Cd*+, and Pb*+ impurities for Ag+ ions computed at various positions relative to the twin planes. At the Ag+ twin plane in AgCl, there is a small preference for Pb*+ to segregate near the twin plane, but this is not true for Zn*+ and Cd*+. Near the Cl- twin plane, there is an energetic preference for all of these ions to segregate. It is difficult to make any generalization based on these results because several effects, including size of the impurity, the distortions near the twin plane, and the variations in potential might be operating here. Defects near the double twin plane described in eqn (3) have been studied. For AgCl, using the CCHJ III potential, the energy of formation of this stacking arrangement is 0.404 J/m*, which is approximately two times larger than the comparable twin plane energies of formation in Table 2. Thus, this ‘double’ stacking fault is considerably less likely than the twinplane arrangement. Formation energies of Ago in the double twin region are about the same as the bulk, so there is no preference for Ago. There is a preference for Cl0 formation in this region by 0.3 eV versus the bulk.
We have found that energy is required to form twin planes relative to the perfect crystal. The formation energy per unit area is roughly comparable for Cland Ag+ twin planes in AgCl, but smaller for Br than Ag+ twin planes in AgBr. These formation energies may be compared with corresponding values in other materials. In NaCl { 11I} stacking fault energies are calculated [22] to range from 0.24 to 0.81 J/m’ versus our computed twin-plane energies of 0.23 J/m* for AgCl and 0.18 J/m* for AgBr. Other alkali halide stacking fault energies are a few times larger for Li salts with small halide ions and smaller for Rb salts with larger halide ions. There are no experimental data available for comparison. The surface energy of {ill} AgBr was previously [8] calculated to be 0.58 J/m*, which seems to be reasonable relative to the twin-plane energy, because the surface is a much more drastic discontinuity. Comparison of the difference in lattice energy of a supercell containing one twin plane to the lattice energy of a supercell of perfect silver halide gives a value of approximately 1% of the crystal energy, indicating the rather small formation energy of this stacking fault. Summing up, our comparisons of stacking fault energies of twin planes to other calculations are reasonable, but there are no good experimental data for comparison. One may ask how twin planes grow during solution deposition on {11 I} surfaces. Of course, the exact structure of the {Ill} surface is poorly defined, although some models [8, 231 have been advanced. In any case, the top surface, while incomplete,
Computations of properties of twin planes in silver halide contains ions of all one type. Growth of a second layer on this surface probably proceeds in a layer-by-layer mode. When the incoming ions bind to a site, they are in equilibrium with the liquid phase so that reversible adsorption-desorption is occurring. Once an ion has remained on the surface sufficiently long enough for subsequent ions to bind around it, a patch of ions is created with the { 111) registry. Thus, all that is required to start this process is that the starting ion bind in the wrong hollow site (i.e. the site leading to twin planes). We note that earlier calculations [8] have shown that the hollow site is the preferred binding site for adions, as expected from general considerations of their closed-shell, spherical nature. This overall mechanism seems to be a likely mode of formation of twin planes. Steps that lead to slower growth should reduce the occurrence of twin planes if this mechanism is right. The calculations predict that Br- twin planes would be predominant in AgBr, because Ag+ twin planes have somewhat larger formation energies. The difference in formation energy, however, is of small enough magnitude so that both types of twin planes could be formed. For AgCl, the differences are even smaller and it is likely that both planes could coexist. Indeed, models containing a jog on the twin plane have been proposed [9] that would possess both types of twin plane. The Madelung potentials clearly indicate deeper levels for electrons at Ag’ twin planes than the bulk of AgCl or AgBr. Holes have a potential of about 0.2eV more favorable for trapping at halide twin planes than bulk in both AgCl and AgBr. The range of these effects is very small, extending less than one lattice constant normal to the twin plane. These effects might reduce transport of photocarriers across the twin plane interface. This indirect deduction concerning the effect of twin planes upon carrier mobility depends upon the delocalized character of the carrier. We estimate that the trap depth of a 258 radius polaron is only a few meV based upon the weighted volume fraction of the twin plane. Such delocalized species should experience only a minor perturbation due to the twin plane. On the other hand, a Ago atom would have a trap depth of a few tenths of an eV. Thus, the effect of the twin plane on mobility depends strongly on the size of the carrier. Localized defects such as Ago or Bra show a preference for location on or near twin planes in accord with the Madelung potential considerations just discussed. The magnitude of the effect is reduced, though, because of the strong interaction with the lattice. Ionic point defects have lower formation energies near the twin plane. This probably arises because of the lattice distortions in this region of the
633
crystal. This effect is true for both silver ion vacancies and interstitials, so it is unlike a space charge layer. An effective reduction of about 0.4eV in Frenkel defect energy is computed in AgCl and AgBr, so that there could be a significant increase in concentration of both point defects right near the twin plane as compared to the bulk. One proposal [6] that was advanced earlier for twin planes is that interstitial silver ions adjacent to the twin plane could be easily reduced to Ago in this region of structural disorder. We have examined this effect computationally for AgCl by determining the energy required to convert an interstitial silver ion to an atom. The only significant effect is at the silver ion twin plane, where the required energy is 1.14eV compared to the corresponding value 1.80eV in the bulk. This value is also significantly less than energies for conversion of Ag+ to Ago at a lattice site, as shown in Table 5. Thus, the Ag+ twin plane could act to concentrate both electrons and interstitial silver ions leading to Ago formation. It is interesting that this mechanism operates without a partial charge, as is invoked for surface [24] mechanisms of latent image formation involving defects such as kinks.
5. CONCLUSIONS This report has involved a first attempt to calculate the electronic properties of twin planes in silver halide. It has shown that there are significant differences in the hole and electron trapping properties of silver or halide twin planes. Based on energy differences that are small, both types of twin planes seem possible, but the halide form is most stable. The silver twin plane has a Madelung potential reduced from bulk values by 0.4-0.5V, which accounts for its enhanced electron trapping properties. Support is given for a proposal suggesting easier reduction of interstitial silver ions to atoms in the presence of a silver ion twin plane. Acknowledgements-1 am grateful to Al Marchetti, Ken Lushington, Ray Eachus, and Sam Chen for valuable discussions.
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